60 = a * (-30)^2
a = 1/15
So y = (1/15)x^2
abc)
The derivative of this function is 2x/15. This is the slope of a tangent at that point.
If Linda lets go at some point along the parabola with coordinates (t, t^2 / 15), then she will travel along a line that was TANGENT to the parabola at that point.
Since that line has slope 2t/15, we can determine equation of line using point-slope formula:
y = m(x-x0) + y0
y = 2t/15 * (x - t) + (1/15)t^2
Plug in the x-coordinate "t" that was given for any point.
d)
We are looking for some x-coordinate "t" of a point on the parabola that holds the tangent line that passes through the dock at point (30, 30).
So, use our equation for a general tangent picked at point (t, t^2 / 15):
y = 2t/15 * (x - t) + (1/15)t^2
And plug in the condition that it must satisfy x=30, y=30.
30 = 2t/15 * (30 - t) + (1/15)t^2
t = 30 ± 2√15 = 8.79 or 51.21
The larger solution does in fact work for a tangent that passes through the dock, but it's not important for us because she would have to travel in reverse to get to the dock from that point.
So the only solution is she needs to let go x = 8.79 m east and y = 5.15 m north of the vertex.
Answer:
23.6 or A
Step-by-step explanation:
We have sin already. 8/20
We use inverse sin of 0.4 (8/20)
The answer of inverse sin is 23.57817848
or 23.6
Answer:
2.04 seconds
Step-by-step explanation:
Falling objects near the surface of the earth have an acceleration of -9.81 m/s².
Acceleration is the change in velocity over change in time:
a = (v − v₀) / t
-9.81 = (-30.0 − (-10.0)) / t
-9.81 = -20.0 / t
t = 2.04
It takes 2.04 seconds.
Answer:
Step-by-step explanation:
The average rate of change is the change in the number of visitors divided by the change in the number of months.
1. Change in number of visitors
Change in visitors = 182 -125 = 57 visitors
2. Change in number of weeks
Change in time = 5 - 2 = 3 months
3. Average rate of change
Answer:
2,800
Step-by-step explanation:
Because they are adding 700 each time.
